Problem 47 - Algebra A Combined Function

Question

Simplify each expression. \(-6-(2-11)\)

Step-by-Step Solution

Answer

The simplified expression is 3.

Step 1: Understand the Expression

We need to simplify the expression \(-6-(2-11)\). This expression involves subtraction and requires us to carefully deal with the parentheses first.

Step 2: Simplify Inside the Parentheses

Inside the parentheses, the expression is \(2 - 11\). Calculate this by subtracting 11 from 2.\[2 - 11 = -9\]

Step 3: Substitute Back into the Expression

Replace the original parentheses in the expression with the result from Step 2. The expression now becomes\(-6 - (-9)\).

Step 4: Simplify the Expression

Subtracting a negative is the same as adding the positive equivalent. So, \(-6 - (-9)\) becomes \(-6 + 9\).Calculate: \(-6 + 9 = 3\).

Key Concepts

Simplifying Expressions

When we're working with expressions, our main goal is to make them as simple as possible. This is known as simplifying expressions. It means transforming a complex equation into a more readable and straightforward form.
Sometimes, expressions include parentheses, like in \(-6 - (2-11)\). Prioritize operations inside the parentheses first. Simplifying doesn’t change the expression's value; it only makes it easier to read and understand.

• Step inside any parentheses first.
• Convert double negatives, for instance.
• Combine like terms if possible.

In our example, simplifying means first dealing with \(2 - 11\), which becomes \(-9\). Replace the original parentheses with this result to obtain a much simpler problem to solve.

Subtraction with Negatives

Subtraction becomes more interesting when dealing with negative numbers. The key is understanding that subtracting a negative is the same as adding a positive.
For example, in the expression \(-6 - (-9)\), we're effectively adding. Understanding this rule helps in many algebraic problems:

• Think of a minus sign in front of a negative as reversing the number’s sign.
• Convert it into an addition problem when seeing two consecutive negative signs.

With \(-6 - (-9)\), transform it into \(-6 + 9\) and then calculate the result.
This strategy turns potentially confusing operations into simpler addition.

Order of Operations

When simplifying expressions, knowing the right order for operations is crucial. This is often remembered by the acronym PEMDAS, which stands for

• Parentheses
• Exponents
• Multiplication and Division (from left to right)
• Addition and Subtraction (from left to right)

To solve our example, \(-6 - (2-11)\), begin with the parentheses. First subtract inside, \(2 - 11 = -9\), then move on to replacing the parentheses.
This sequence ensures accuracy. Work through each layer of calculation without skipping or rearranging steps, as it maintains the integrity of the expression.
Besides simplifying expressions properly, mastering the order of operations ensures you won't make mistakes when tackling complex equations.